9-€-~-__,. -' '~a.<:_ ~_.e_i- 4 c~ ~l--l-~~ ~. ~/26~-.S /Ze-/· -_osc - ~ ... #s # / 2.7 .s ·
Department of the Navy Bureau of Ordnance Contract NOrd 9612
T-ER~INAL SINKING VELOCITIES FOR A SERIES
0~' FLAT NOSED BODIES
,I
A Hi g h S p e e d W a t e r -T u nne 1 Study
R. L. Waid
' ' I I
Hydrodyriam;cs ~aboratory California Institute of Tec;hnology
Pasadena, California
Project Supervisor J. T. McGraw
T Report No'. E-12.10 , November 195 2
Copy No._£:/:__
I <
Approved by: M. S. Plesset
SUMMARY
Drag studies were made on a series of models having varying de
gree s of bluntness and varying length-to-diameter ratios. Using the
drag coefficients obtained from the tests, terminal sinking velocities in
sea water were calculated for various volumes and de ns ities. It was
found that the terminal sinking velocity of a blunt-nosed body could be
increased 15 percent if the length-to-diameter ratio was increased from
7 to 14 for the same volume. The terminal sinking v e locity of a fine
nosed body could be increased only 2 percent if the length-to-diameter
ratio was increased from 6 to 12.
INTRODUCTION
Drag tests were made in the High Speed Water Tunnel on a series
of bodies of various nose bluntness for several length-to-diameter ra
tios. These tests were conducted as part of a program to develop high
terminal sinking velocity shapes.
Previous studies':' hc:.d been. made on a series of blunt nosed 1** ' bodies. Because of the interest in flat nose bodies to facilitate water
entry, the present series of tes-ts was made on bodies having various
nose bluntness ratios. The nose bluntness ratio is the ratio of the flat
nose diameter to the maximum body diameter. The length-to-diameter
ratio was varied for each nose bluntness to determine the slenderness
which would produce the greatest terminal sinking velocity.
MEAS U.REMEN TS
The 2-in. diameter models used for the tunnel drag studies con
s i sted of 9-caliber ogive noses, cylindrical center sections and Lyons
Forrr1 A 2
afterbodie s with shrot;.d ring tails.
The model noses were progressively truncated from a pointed
nose to a nose with a l. 5-in. diameter flat. For each nose bluntness
the length of the model was varied from approximately 12 in. to about
28 in. The complete model series covered length-to-diameter ratios
of 6 to 14 for nose bluntness ratios of 0. 00 to 0. 75. Figure 1 shows the
models for a nose bluntness range of 0. 00 to 0. 75 for a length-to
diameter ratio of 10, and Fig. 2 for a nose bluntness of 0. 50 for a range
of length-to-diameter ratios of 6. 445 to 14. The velocities used for the
drag tests covered a range from 5 to 80 fps.
Pitching moment readings were taken3
along with the drag data
so tha t corrections could be rnade to e liminate the errors inherent in
the High Speed Water Tunnel balance resulting from the interaction of
pitching moment on drag force.
':'Tests wer e rr1ade on several of the previously tested models to check the effect of the interaction of pitching moment on the force measurements. 3 Small discrepancies in the drag coefficient (on the order of 5 percent) have been observed. However, the previously reported trends have been substantiated.
>'.o:' See bibliography on page 4.
-2-
Drag coefficients based on cross section area were calculated
and plotted as a function of Re ynolds- number based on the over-all
length. Figure s 3 and 4 show these curves for the representative
series of models shown in F i g s. 1 and 2 . Solid line s denote experi
m e ntal curves, whereas dotte d lines denote extrapolation. The curve
for the body with a pointed nose is considered not to be as accurate as
the other curves. All attempts to produce a turbulent boundary layer
on this pointed nose model caused a definite increase in the drag coef
ficient. It is b e lieved that the increase in the drag coefficient was
caused more by the drag of the turbulence producing material than by
any effects that the material had on the boundary layer . The results
for the other models are all considered to be satisfactory.
CALCULATED TERMINAL SINKING '/ELOCITY
The drag coefficient curves were extrapolated parallel to the
Schoenherr skin friction curve. This technique assumes that the form
drag of the bodies is constant within the range of the Reyno~ds numbers
tha t are involved (106
to 108
).
Te rrninal sinking velocities were calculated for all of the rrwde l
configurations. Figure 5 shows the results of these calculation s for
a hypothetical projectile having the volume (0.3825 cu ft) and the density
in air {169.5 lb per cu ft) of the 6-in. Projector Charge, Ex. 1 {Bu.Ord
Sketch No. 239308). The curve for the projectile with the pointed nose
is not considered to be accurate because of the previously mentioned
experimental difficulties.
It is to be noted that over the range of variables shown in Fig. 5
there are no optimum length-to-diameter ratios. Consequently, for
this configuration it is impossible to specify optimum design character
istics for a free sinking projectile within the limits of this experimental
investigation. It should be note d, however, that for a given nose blunt
ness the highest tenninal sinking velocity is attained by the more slender
(greater length-to-diameter ratio} configuration. This feature is more
pronounced for the blunt nosed shapes. A 15 percent increase in sinking
velocity can be obtained by changing the length - to-diameter ratio from
-3-
7 to 14 for the configuration with a 0. 75 nose bluntness. Ten p e rcent of
this increase is caused by changing the ratio f r om 7 to l 0. The change
from a length-to-diameter ratio of 10 to 14 produces only an additional
5 percent improvement in the sinking velocity. The fine nosed bodies
show as little as 2 perc e nt increase over the same range. The pre
viously reported t e rminal sinking velocity of the 6-in. Projector
Cha rge Ex. l is plotted for comparison in Fig. 5. It has a nose blunt
ness of 0. 50 a nd a length-to-diameter ratio of 7. 3.
The result of a t l::! st on a finless projectile configura tion of 0. 625
nose bluntne ss ratio a nd a length-to-diameter ratio of 7 is plotted in
Fig. 5. It is of interest to note that the removal of the fjns results in
a 5 perc e nt incr ease in the terminal sinking velocity.
EFFECT OF VOLUME AND DENSITY ON TERMINAL SINKING VELOCITIES
Terminal sinking velocities of a projectil e of 0.50 nose bluntness
rat io were calculated for :1 series of volumes and densities.
Figure 6 shows the effect of length-to-diameter ratio on the
terminal sinking velocity of a projectile of constant volume for var i
ous ,densitic s. The highest sinking velocity is attained by the more
sle nder configurations. The increase in sinking velocity produc e d by
changing the l e ngth-to-diameter ratio from 7 to 14 is 15 percent for
a density of l 00 lbs per cu ft, decreasing to l 0 percent for a den s ity
~f 250 lbs per cu ft.
Figur e 7 shows the e ffec t of the length-to-dia mete r ratio on the
terminal sinking velocity of a proj e ctile of constant density for vari
ous volumes. The more slender configuration {L/D of 14 as com
pared to 7) result s in a l 0 percent increase in terminal velocity for
all volumes.
Figures 8 a nd 9 a r e plotte d from the curves in Figs. 6 a nd 7,
respectively. The effect of density and volume on the terminal ve
locity is shown for se v e ral length-to-diameter r atios.
Practica l des ign considera tions m a y requir e a proj ec tile which
has a configuration which is less slender than the ideal shape. It is
-4-
of considerable interest to know what penalty occurs when designing a
way from an optimum configuration. The curves in Fig. 8, for example,
indicate that a projectile with a length-to-diameter ratio of 10 or more
suffers a velocity penalty of less than 3 percent when compared with
oBc with a ratio of 14. However, a drag penalty of 11 percent occurs
if the ratio is as low as 6.445 compared with one of 14. For blunt nosed
bodies it appears that a moderately slender projectile configuration
(length-to-diameter ratio of 10) can be nearly as effective as more
slender configurations.
BIBLIOGRAPHY
1. Kermeen, R. W., "Resistance Tests on a Series of Blunt Nose Bodies, The 6 -in. Projector Charge, The 5 -in. A. S. Projectile", California Institute of Technology, Hydrodynamics Laboratory, Memo. Report EM -12. 2, Aug. 28, 1951.
2. Lyons, Hilda M., "Effect of Turbulence on Drag of Airship Models" Air Ministry, Air Research Committee, Reports and Memorandum No. 1511, August 1932.
3. Kermeen, R. W. , "Pitching Moment Balance for the High Speed Water Tunnel", California Institute of Technology, Hydrodynamics Laboratory, Memo. Report EM-12.4, Aprill5, 1952.
4. Kermeen, R. W., "Resistance Tests on the 5-in. A. S. Projectile and the 6 -in. Projector Charge", California Institute of Technology, Hydrodynamics Laboratory, Report No. E-12. 5, April 15, 1952.
-5-
Pointed nose - Turbulence stimulator (Glass beads)
0. 125 Bluntness ratio
0. 250 Bluntness ratio
0. 375 Bluntness ratio
0. 500 Bluntness ratio
0. 625 Blu·•! ·1e ss ratio
0 . 750 Bluntness ratio
Fig. l -A series of representative models with various nose bluntness ratios for a length-to-diameter ratio of l 0.
DENT
-6-
6. 445 length-to-diameter ratio
8 length-to-diameter ratio
10 length-to-diameter ratio
12 length-to-diameter ratio ·
14 length-to-diameter ratio
Fig. 2 -A series of representative models with various length-todiameter ratios for a nose bluntness ratio of 0. 50.
0 C>
1.0
...: .40 z w C> li: 1..1.. w 0 C>
(!) <( a: 0
.10
1-
--1----r-
-7-
NOSE BLUNTNESS RATIO-
,..... i---- --1--1--
1-1- --- --+---1--
r--1--r- ---::::::: --1---"--1--r- f-1- --- - i---r- j;;.,--~
1--
t- ------=- f:::_-:;:.. ~ t-~-
REYNOLDS NUMBER (BASED ON LENGTH)
~ ~
1-- .750
1- .J2J I I
f-. .500
I I f-. .375 ;....._ .250 - 125 - 1-1\ 0 - f--
Fig. 3 - Drag coefficients based on cross section area for a series of models of various nose bluntness ratios for a length-to-diameter ratio of 10.
1.0
0 C>
1-.40
z w LENGTH- TO- DIAMETER RATIO- \ C> li: 1..1.. w 0 C>
(!) <(
-r--- \ - i--- ...... 1-t----t--- 1--1- 1-~----+--- - i-- t--- t--_ 14 -- - 12- f--1-- 1-1- --I-- -1-- 10
1-- --- --I--i--1- 8 1-~-----+--- i-- i--- 6.445 a: 0
.10
REYNOLDS NUMBER (BASED ON LENGTH)
Fig. 4 -Drag coefficients based on cross section area for a series of .models of various length-to-diameter ratios for a nose bluntness ratio of 0.50.
ONFIDEN
70
60
0 z 0 50 u
"' (/)
"' "' Q_
1-
"' "' "-
>- 40 !::: (.)
0 ...J w > (!)
z ;;:: ~ <J) 30
...J <X z :::!! a: w I-
20
10
0 0
-8-
I I 1 I I I I BODY CONFIGURATION
NOSE I CENTER I AFTERBODY
1 TRUNCATED 91 CYLINDRICAL I LYONS FORM + CALIBER OGIVE FINS AND SHROUD
I I I I I I r I 1 1 I I
N. B. R. = NOSE BLUNTNESS RATIO= FLAT NOSE DIAMETER _ v MAXIMUM DIAMETER /
4
.125~ 1- 0 (POINTED NOSE)
1-- .250
I ll / - 3r ----0: ::-- I lj - -- .510 ... ------:r ~~ - I
v-- -- .625
"?/ 0
lr ~) PROJECTOR CHARGE, EX . I 0 - -- .750
~I N.B R. • 5: ______.--
H /
7
I
I
8 16
LENGTH - TO- DIAMETER
12
RATIO (..h..) D
20
Fig. 5 - The effect of length-to-diameter ratio on terminal sinking velocity for a series of projectiles of various nose bluntness ratios. (Same volume and density as 6-in. Projector Charge Ex. l .
Vol. = 0. 3825 cu ft; Density = 169. 5 lbs/ft3.)
C>N-FlDEN..T
70
60
0 z 0 50 u w (/)
a: w Q.
,__ w w lL
>- 40 ':::: (.)
0 ...J w >
<.? ~ :.:: z (f) 30
...J <t z :::;; 0:: w 1-
20
10
0 0
- 9-
\ DENSITY IN AIR (LBS / FT 3 )
. .J--!---
1\ v v
4
250
l----l-----v 200 v 1---
---l----
169 .5 v - 1---
v ~ 140
1---
~ l----
120
1---l----~ 1..----100
8
LENGTH - TO - DIAMETER
12
RATIO
--
-
--
--
--
--
(...!::..) D
16 20
Fig. 6 - The effect of length-to-diameter ratio on terminal sinking velocity of a projectile of 0. 5 nose bluntness ratio for various densities.
(Same volume as 6-in. Projector Charge Ex. l. Vol. = 0 . 3825 cu ft.)
70
~
60
0 z 0 50 u w
"' 0:: w 0..
f-w w u.
>- 40 ':::: (..)
0 _J
w > C)
z ;;;::: z Vi 30
_J <[ z ::;: a: w 1--
20
10
0 0
-10-
/ v-
-VOLUME (CUBIC FEET)
~ L_
l';o /v
/ ~
f..---
2.0/
.....----v .....
1.0/ L.-:::::: -
I v 0.61/ ......---),...----
0382~ ~
4 8 12
LENGTH - TO- DIAMETER RATIO (.h..) 0
16
Fig. 7 - The effect of length-to-diameter ratio on terminal sinking velocity of a projectile of 0. 5 nose bluntness ratio for various volumes.
(Same density in air as 6-in. Projector Charge Ex. l. Density = 169. 5 lbs/ft3 .)
-11-
60 0 z 0 <.> w Vl
lo-r--~ 0:: w ()._
t-w w 40 lL
>-!::: u 0 _J
w >
(!)
z 20 ;;<' z Vl
_J
~ ~ 6.445
~
~ v /
0 6" PROJECTOR CHARGE, EX. I
~ ~v
lr <[ z ~ tr w I-
) 0
0 50 100 150 200 250
DENSITY IN AIR (POUNDS PER CUBIC FOOT)
Fig. 8 - The effect of density on the terminal sinking velocity of a projectile of 0. 5 nose bluntness ratio for three length-to-diameter ratios.
(Same volume as 6-in. Projector Charge Ex. l. Vol. = 0.3825 cu ft.)
0 z 0 <.> w Vl
a: w ()._
t-w w lL
>-!::: u 0 _J
w >
(!)
z :;;: z (f)
_J <[ z ::;; tr w I-
80
60
40
20
0 0 .1
/~ :::: ::::: / /~
~ -;::; /
/
~ v ....... ..........
~ I--
0 6" PROJECTOR CHARGE, EX. I
0.4 1.0
VOLUME ( FT')
/ J I ;: / 10
r::: I
/ / / 6.;45
/ v L _) 0
4.0 10
Fig. 9 - The effect of volume on the terminal sinking velocity of a projectile of 0. 5 nose bluntness ratio for three length-to-diameter ratios.
(Same density in air as 6 -in. Projector Charge Ex. l. Density = 169. 5 lbs/ft3 .)
•
... .
Copy No.
1
2
3-4
5-7
8-12
13-15
16
17-18
19-20
21
22-23
2.4-26
Z7
28
29
30
31~32
Chief,
Department of the Navy Bureau of Ordnance Contract NOrd 9612
DISTRIBUTION LIST
Bureau of Ordnance, Navy Dept., atten: Code Re6a
Chief, Bu1·eau of Ordnance, Navy Dept., atten: Code Re3d
Chief, Bureau of Ordnance, Navy Dept., atten: Code Ad3
•
Washington, D.C.
Washington, D.C.
Washington, D.C.
Chief, Bureau of Aeronautics, Navy Dept., Washington, D. C. atten : Code De3
Chief, Bureau of Ships, Navy Department, Washington 25, D. C.
Chief of the Office of Naval Research, Navy Dept., Washington, D. C., Code 438
Office of Naval Research, Los Angeles Branch, l 030 East Green Street, Pasadena, California
Director, David Taylor Model Basin, Washington 7, D. C.
Commanding Officer, Naval Torpedo Stati,cm, . Newport, R.I.
Commander, Naval Ordnance Test Station, Inyokern, China Lake, California. Atten: Technical Library, Code 5507
Commander, Naval Ordnance Laboratory, White Oak, Silver Spring 19 , Maryland
Ofiicer-in-Charge, Pasadena Annex Naval Ordnance Test Station, Inyokern, 3202 East Foothill Blvd., Pasadena, California, atten; Pasadena Annex Library, Code P5507
Director, Expe rimenta1 Towing Tank, Stevens Institute of Technology, via: Bureau of Aeronautics Representative, c/o Bendix Aviation Corp., Eclipse -Pioneer Division, Teterboro, New Jersey.
Director, Ordnance Research Laboratory, Pennsylvania State College, State College, Pennsylvania
Alde n Hydraulic Laboratory, Worcester Polytechnic Institute, Worcester, lviass., via: Inspector of Naval :tvlaterial, 495 Summer St., Boston l 0, Mass .
In spe ctor of Naval Material, Development Contract Section, 1206 South Santee Street, Los Angeles, Califo rnia
Superintendent, U.S. Navy Postgraduate School, Annapolis, Maryland.
Copy No.
33-34
35-44
45
46
47
48
Department of the Navy Bureau of Orunance Contract NOrd 9612
Distribution List (Cont1 d)
Director, U.S. Naval Electronics Laboratory, Point Lorna, San Diego, California
British Joint Services Mission, Navy Staff, via: Chief, Bureau of Ordnance, Navy Dept., Washington 25, D. C., atten: Code AD8
Executive Secretary·, Research and Development Board, National Defense Building, Washington, D. C.
Dr. E. Bromberg, Office of Naval Research, Mechanics Branch, Washington 25, D. C.
Commander, Submarine Development Group TWO, Box 70, U.S. Naval Submarine Base, New London, Conn.
Dr. F. C. Lindvall, 200 Throop, California Institute of Technology, Pasadena, California
![· 4-= = 96, ., / 7gh, 7 4#b= 1 2 4c ; %7ghb=. a , =i4 / 96,@. 9|a6,+9 b= 9 e) /? a.,+96, 4#? %?,m v96, =% ] %4 .,+9 b= 9 a, +9?,8a 4#,+9 e k h a/ 7,8/a =0 5; % b=]h](https://static.documents.pub/doc/80x56/5c4df16f93f3c304f47b85b3/-4-96-7gh-7-4b-1-2-4c-7ghb-a-i4-96-9a69-b-9-e.jpg)
